Reducing θ_13 to 9 degrees

We propose to consider the possibility that the observed value of $θ_{13}$ is not the result of a correction from an initially vanishing value, but rather the result of a correction from an initially larger value. As an explicit example of this approach, we consider analytically and numerically well-known CKM-like charged lepton corrections to a neutrino diagonalization matrix that corresponds to a certain mixing scheme. Usually this results in generating $θ_{13} = 9^\circ$ from zero. We note here, however, that 9 is not only given by $0 + 9$, but also by $18 - 9$. Hence, the extreme case of an initial value of 18 degrees, reduced by charged lepton corrections to 9 degrees, is possible. For some cases under study new sum rules for the mixing parameters, and correlations with CP phases are found.

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